X-ray observations of EXO 0748–676 during thermonuclear bursts revealed a set of narrow (Δλ/λ = 0.018) absorption lines that potentially originate from the stellar photosphere. The identification of these lines with particular atomic transitions led to the measurement of the surface gravitational redshift of the neutron star and to constraints on its mass and radius. However, the recent detection of 552 Hz oscillations at 15% rms amplitude revealed the spin frequency of the neutron star and brought into question the consistency of such a rapid spin with the narrow width of the absorption lines. Here, we calculate the amplitudes of burst oscillations and the width of absorption lines emerging from the surface of a rapidly rotating neutron star for a wide range of model parameters. We show that no combination of neutron star and geometric parameters can simultaneously reproduce the narrowness of the absorption lines, the high amplitude of the oscillations, and the observed flux at the time the oscillations were detected. We, therefore, conclude that the observed absorption lines are unlikely to originate from the surface of this neutron star.